Universal Modified Newtonian Dynamics Relation between the Baryonic and 'Dynamical' Central Surface Densities of Disc Galaxies

摘要

I derive a new modified Newtonian dynamics ( MOND) relation for pure-disc galaxies: The "dynamical" central surface density, Sigma(0)(D), deduced from the measured velocities, is a universal function of only the true, "baryonic'' central surface density, Sigma(0)(B): Sigma(0)(D) = Sigma S-M(Sigma(0)(B)=Sigma(M)), where Sigma(M) = a(0)/2 pi G is the MOND surface density constant. This surprising result is shown to hold in both existing, nonrelativistic MOND theories. S(y) is derived: S(y) = integral(y)(0) v(y')dy', with v(y) being the interpolating function of the theory. The relation aymptotes to Sigma(0)(D) = Sigma(0)(B) for Sigma(0)(B) Sigma(M), and to Sigma(0)(D) = (4 Sigma(M)Sigma(0)(B))(1/2) for Sigma(0)(B) Sigma(M). This study was prompted by the recent finding of a correlation between related attributes of disc galaxies by Lelli et al.. The MOND central-surface-densities relation agrees very well with these results.